A detailed quantitative description of fluid flow in small diameter, porous tubes is of obvious interest to renal physiologists, among others. To date, analytical solutions have been presented only for special cases of the viscous flow problem (Macey 1963; 1965), and stable numerical solutions have been developed only for relatively large Reynolds numbers (Hornbeck, et al., 1963). Preliminary results indicate that an analytical solution of the Navier-Stokes equations is possible if certain assumptions applicable to biological situations are made. (See accompanying Appendix). This analytical solution will be used in conjunction with simple model systems to study (1) the possibility that viscous effects contribute to the phenomenon of renal glomerular tubular balance and (2) the possibility that pressure and viscosity play significant roles in initiating renal medullary counter-current multiplication, as well as counter-current multiplication in other physiological systems.